To "time shift" a broadcast AV
signal is to store it for later enjoyment. This normally means that you use a VCR
to record a television
program, or a tape deck to record a radio
The beauty of the term is that it makes the activity seem much less like nasty old copyright theft. No-one could seriously object to time shifting, could they? In fact, the infamous betamax case (Sony Corp. v. Universal City Studios 1983) established it's legality, at least as far as recording tv shows is concerned.
And yet you can't save Real Audio Streams.
Contrast space shift